Method and computer program for predicting bilirubin levels in neonates

ABSTRACT

The invention relates to a method and a computer program for estimating a bilirubin level of a neonate, composed of the steps of:Acquiring a series of bilirubin levels estimated at different time points from a sample obtained from a neonate,Acquiring a plurality of covariates from the neonate, each composed of an information about a neonatal property,Providing a pre-defined bilirubin model function, wherein the bilirubin model function is configured to describe a time course of a bilirubin level of a neonate,Determining a plurality of model parameters of the bilirubin model function, wherein each model parameter is estimated from at least one covariate of the plurality of covariates and an associated population model parameter,Determining from the series of acquired bilirubin levels and the bilirubin model function with the determined model parameters an expected bilirubin level of the neonate for a time particularly later than a lastly acquired bilirubin level of the series of bilirubin levels.

CROSS REREFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser.No. 16/651,992 filed on Mar. 27, 2020, which is a United States NationalStage Application under 35 USC § 371 of International Application No.PCT/EP2018/076325 filed Sep. 27, 2018, which claims priority to EP17194160.2 filed Sep. 29, 2017, the contents of each of which areincorporated herein by reference.

SPECIFICATION

The invention relates to a method and a computer program for estimatinga time course of a bilirubin concentration of a neonate.

Physiological jaundice is the most prevalent clinical conditionoccurring during the first days of life, with higher incidence inpreterm than term neonates. It is caused by an abnormally high level ofbilirubin, a byproduct of red blood cells (RBCs) decomposition and orimmature metabolism and elimination of bilirubin during the first daysof life. Increased serum bilirubin levels occur in literally everyneonate, while in 5%-10% of them an intervention is needed.

Phototherapy is the standard of care, but there is no clear quantitativemethod to optimize its delivery. Some risk factors for development ofhyperbilirubinemia have been described, such as gestational age (GA),blood group incompatibility, breastfeeding or excessive weight loss.Failure to promptly identify infants at risk for developing severejaundice can lead to life-long neurologic consequences. Thus, neonatalhyperbilirubinemia requires close monitoring and increased medicalvigilance which, in turn, may result in delayed hospital discharge or inreadmission of an otherwise healthy neonate.

In clinical practice, a single bilirubin measurement is currentlyinterpreted using specific bilirubin charts, which compare the acquiredbilirubin level at a given time-point to the distribution of bilirubinin a population of reference. The major limitation of this currentstatic approach is the use of only one single bilirubin measurement at agiven time point, which does not take into account the dynamics ofbilirubin. This leads to inaccuracies, as this approach relies on asingle concentration at which the measurement is prone to inter- andintra-individual variability.

In addition, with these bilirubin charts, it is difficult to account formultiple risk relevant factors.

Therefore, the problem underlying the invention is to provide a methodfor accurately estimating future bilirubin levels (i.e. forecastingindividual bilirubin time course) in a neonate as well as for accountingfor and quantifying the influence of phototherapy on a neonate.

This problem is solved by a method according to claim 1 and a computerprogram according to claim 14.

Advantageous embodiments are described in the subclaims.

According to claim 1 a method for estimating, particularly predicting orforecasting an expected bilirubin level of a neonate, comprises thesteps of:

-   -   Acquiring a series of bilirubin levels, such as bilirubin        concentrations or bilirubin amounts, estimated at different time        points particularly from a sample obtained from a neonate,    -   Acquiring a plurality of covariates from the neonate, each        comprising a particularly numeric or logic information about a        maternal or a neonatal property,    -   Providing a bilirubin model function, wherein the bilirubin        model function is configured to characterize a time course or        dynamics of the bilirubin level of the neonate,    -   Determining a plurality of model parameters of the bilirubin        model function, wherein each model parameter is estimated from        and is particularly a function of at least one covariate of the        plurality of covariates and particularly a pre-defined,        associated population model parameter, wherein particularly a        population model parameter distribution is associated to each        population model parameter,    -   Determining from the acquired series of bilirubin levels and the        bilirubin model function with the determined model parameters an        expected bilirubin level of the neonate for a time particularly        later than a lastly acquired bilirubin level of the series of        bilirubin levels.

The method with these features solves the problem according to theinvention.

According to an alternative or to an additional aspect of the invention,the method for estimating a bilirubin level of a neonate comprises thesteps of:

-   -   Acquiring a series of bilirubin levels estimated at different        time points from a neonate, particularly wherein at least one        time point lies prior to a particularly first phototherapy of        the neonate,    -   Acquiring a plurality of covariates from the neonate, each        covariate comprising an information about a neonatal property,    -   Providing a predefined bilirubin model function, wherein the        bilirubin model function is configured to describe a time course        of the bilirubin level of the neonate,    -   Determining a plurality of model parameters of the bilirubin        model function with an incorporated combination of covariates of        the plurality of covariates on associated population model        parameters,    -   Determining from the acquired series of bilirubin levels and the        bilirubin model function with the determined model parameters an        expected bilirubin level of the neonate for a time later than a        lastly acquired bilirubin level of the series of bilirubin        levels.

The following embodiments can be applied to and combined with bothembodiments of the method according to the invention.

A bilirubin level can be a bilirubin concentration or an amount ofbilirubin. The acquisition and also the estimation of bilirubin levelsare particularly achieved with state of the art methods. The bilirubinlevels are particularly measured from a blood sample obtained from theneonate. A series of bilirubin levels is therefore a plurality ofbilirubin levels acquired form the same neonate over a time interval.

It is important that the acquired series of bilirubin levels correspondsto different ages, i.e. time points, of the neonate, such thatparticularly a temporal series of bilirubin levels is generated. Thisseries serves as the basis for the estimation of an individual bilirubinlevel prediction.

Without the acquisition of the bilirubin levels, it would not bepossible to estimate a particularly specific time course of thebilirubin level in said neonate, but only a general prediction validonly for a population average would be achievable.

The method is particularly suited for estimating an expected bilirubinlevel in a preterm neonate. However it can also be applied to term andlate term neonates.

A neonate in the context of the specification is particularly a newbornbaby in the first 28 days of life.

Within the group of neonates it can be differentiated between pretermneonates, term neonates and late-preterm neonates.

A preterm neonate in the context of the specification is particularly aneonate born with less than 37 weeks of gestation that is more than 21days before the expected time of birth.

A term neonate in the context of the specification is particularly aneonate born around the expected time of birth with at least 37 weeks ofgestational age.

A late-preterm neonate in the context of the specification isparticularly a neonate born between 34 and 36 weeks of gestation that isbetween 21 and 35 days before the expected time of birth.

Late-preterm neonates have a particularly high risk of bilirubinmorbidity.

According to the invention, a covariate comprises information about aneonatal property. This information is particularly comprised orexpressed in a numerical or logical value that can be used to calculatethe model parameter.

A covariate particularly comprises an information or is a relevantfactor that influences bilirubin changes.

The covariates are particularly a physical property of the neonate, suchas the birth weight, or events that are associated to the neonate, suchas receiving a phototherapy or being born via caesarean section.Therefore, a covariate in the context of the description is notarbitrarily chosen but is a property associated to the neonate. Theacquisition of a covariate can for example be facilitated by a databasequery of the birth record and/or by an interview with a person inpossession of this information.

Covariates are particularly variables that influence the modelparameters of the bilirubin model function. Therefore, the modelparameters can be understood as being depended on the covariate. Themodel parameters particularly are the variables of the model function,wherein the model function directly depends on these model parameters.

The predefined bilirubin model function is configured to model aplurality of bilirubin levels for a plurality of neonates. It isparticularly suited for taking into account an inter-populationvariability as well as differently valued covariates of the pluralityneonates. Thus, the model function is particularly configured to accountfor all variations and deviations of bilirubin levels potentiallyobservable at a neonate at different time points. The model functionparticularly provides a sufficiently high degree of flexibility in orderto describe individual bilirubin levels of a neonate while at the sametime a general bilirubin production and elimination characteristic isvalidly described. Particularly a model function that exhibits thesefeatures (a flexible description of production and eliminationcharacteristics of bilirubin levels) is suited to characterize the timecourse of bilirubin levels.

The covariates particularly account for different subpopulations in apopulation of neonates, wherein the subpopulations exhibit significantdifferently time courses of bilirubin levels, so that the populationaverage time course would not sufficiently well describe the timecourse. The model function according to the invention is particularlyconfigured to model the specific time course of bilirubin level for aspecific neonate, based on the acquired covariates and the modelparameters.

Furthermore, the model function is also configured to take into accountinter-individual variability (IIV). IIV refers to the fact that neonatesof the same subpopulation can exhibit different bilirubin levels andtime courses of bilirubin levels.

A large portion of IIV can explained by different covariates. The morecovariates are identified and quantified the better the prediction offuture or past bilirubin levels according to the model function is.

The method according to the invention is particularly suited to accountfor the IIV and thus to provide an individual estimate for the neonate'sbilirubin levels in the future.

For this reason the model parameters of the bilirubin model function areestimated based on the acquired covariates and the acquired series ofbilirubin levels.

In order to take into account the IIV, the dynamics of bilirubin levelsand to precisely estimate the expected bilirubin level, the methodrequires a series of bilirubin levels of the neonate, rather than just asingle bilirubin level.

Furthermore, each model parameter of the plurality of model parameterscan be estimated from or be a function of a pre-defined, associatedpopulation model parameter. The population model parameter is estimatedparticularly from a plurality of measurements of bilirubin levels from aplurality of different neonates. From such a population of neonates avariety of associated covariates is estimated and eventually apopulation model parameter is determined. The population model parameteris particularly estimated using a so-called population approach. Thepopulation model parameter corresponds to a model parameter for aneonate particularly exhibiting average covariate(s). A model parameterfrom a specific neonate therefore can be calculated by taking intoaccount a deviation of the corresponding covariates from a populationaverage covariate value.

The estimated model parameters as well as the acquired series ofbilirubin levels and particularly a probability distribution for themodel parameters can be processed such that a bilirubin level in thefuture, but also in the past, can be estimated.

The estimation of a future or a past (expected) bilirubin level of theneonate can be done e.g. by using Bayesian statistical methods.

According to the invention by using the information available from apopulation model that has been established previously, the additionalinformation provided by the covariates, and the acquired bilirubinlevels from the neonate or from a sample obtained from the neonate allowfor an accurate estimation of a future and past (expected) bilirubinlevel of the neonate.

According to the invention it is also possible to estimate aparticularly whole time course of expected bilirubin levels

From the population model, a population model parameter set can beestablished, that can be used for estimating the model parameters fromthe covariates.

The dependency of the model parameters from the covariates andparticularly from the population model parameters have to be estimatedquantitatively, particularly prior the method according to the inventionis executed.

In the context of the specification, a model parameter is particularly aparameter that depends on at least one covariate or that is based orderived from at least one covariate.

Therefore, in the light of the current specification, the person skilledin the art will unambiguously acknowledge that a model function mightcomprise also other parameters that are suited and applicable to predictthe expected bilirubin level, wherein said other parameters do notdepend on a covariate.

According to another embodiment of the invention, at least one bilirubinlevel, particularly a plurality of bilirubin levels, of the series ofestimated bilirubin levels is/are acquired prior to an exposure of theneonate to phototherapy. This embodiment allows for the prediction of anecessity for receiving phototherapy and/or an ideal time for receivingphototherapy.

According to another embodiment of the invention, the bilirubin modelfunction is given by a rate equation relating a time-varying bilirubinproduction rate Kprod, with a time-varying bilirubin elimination rateKelim, and particularly a time-varying phototherapy exposure functionPT, wherein the bilirubin production rate Kprod, the bilirubinelimination rate Kelim and particularly the phototherapy exposurefunction PT comprise model parameters from the plurality of modelparameters.

By establishing a rate equation for the bilirubin levels, the processesof bilirubin production and elimination in the neonate are addressedbased on a physics-based medical model.

The rate equation comprises the model parameters, wherein the modelparameters are particularly configured to determine the magnitude of theproduction rate, the elimination rate as well as a potential effect ofphototherapy exposure. The phototherapy exposure leads to a decrease ofthe bilirubin level. Therefore, the function describing the phototherapyexposure will be associated to an elimination process of bilirubin inthe rate equation.

It is of particularly importance to model the processes of bilirubinproduction and elimination as accurate as possible, and also to estimatewhich covariate influences which model parameter.

Once the rate equation with its corresponding model parameters isestablished, a general estimate for neonates regarding a future or pastexpected bilirubin level can be made, if the covariates and theirquantitative influence on the respective model parameter are known.However, without the acquired series of bilirubin levels for thespecific neonate the quantitative prediction remains less accurate.

By accounting for the phototherapy exposure in the rate equation, themethod according to the invention particularly allows for thequantitative estimation of the effect of phototherapy on the bilirubinlevel. Consequently, the method according to the invention is capable ofpredicting the effect of phototherapy on the bilirubin level of aneonate exhibiting a specific set of covariates.

This is not possible with other methods known in the state-of-the-art.

According to another embodiment of the invention, the model function isexpressed as

$\begin{matrix}{{{\frac{d}{dt}Bilirubi{n(t)}} = {{Kpro{d(t)}} - {( {{Keli{m(t)}} + {P{T(t)}}} ) \cdot {{Bilirubin}(t)}}}},} & ( {{Eq}.\mspace{14mu} 1} )\end{matrix}$

wherein

$\frac{d}{dt}$is a derivative operator, and wherein Bilirubin(t) is the bilirubinlevel at a time t.

The time is particularly given with respect to the age of the neonate,particularly in hours or days.

Equation Eq. 1 is a rate equation describing the production andelimination processes as well as elimination processes due tophototherapy accurately.

According to another embodiment of the invention, the production rateKprod(t) is expressed asKprod(t)=Kin _(base)·exp(−K _(PNA) ·t)+KAD,  (Eq. 2)

wherein Kin_(Base) and K_(PNA) are model parameters comprised by theplurality of model parameters, wherein Kin_(Base) is an excess neonatalbilirubin production rate at time zero, wherein KAD is a normalbilirubin production rate, e.g. 3.8±0.6 mg/kg per day [3], as forexample in healthy adults, and wherein K_(PNA) is a decay rate of thebilirubin production rate Kprod(t).

The production rate according to equation Eq. 2 consists of twodifferent terms. A first term comprising the excess neonatal bilirubinproduction rate Kin_(Base) describes the time varying behaviour of theproduction rate of a neonate. As this bilirubin production rate istransient a second term comprising the average production rate of anadult KAD is added to the bilirubin production rate. The averageproduction rate of an adult KAD is particularly not time-dependent.

Also the excess neonatal bilirubin production rate Kin_(Base) and thedecay rate K_(PNA) are particularly not time-dependent. The timedependency of the production rate is of exponential nature.

The excess neonatal bilirubin production rate Kin_(Base) as well as thedecay rate K_(PNA) are model parameters, and therefore dependent on atleast one of the estimated covariate from the neonate.

According to another embodiment of the invention, the bilirubinelimination rate Kelim(t) is expressed as

$\begin{matrix}{{{{Kelim}(t)} = \frac{{KEMAX} \cdot t^{H}}{{T50^{H}} + t^{H}}},} & ( {{Eq}.\mspace{14mu} 3} )\end{matrix}$

wherein KEMAX is a model parameter comprised by the plurality of modelparameters, wherein KEMAX is a maximum stimulation rate of bilirubin,T50 is a time when the bilirubin elimination rate has increased to 50%of its value at t=0, wherein H is a Hill coefficient. T50 isparticularly a model parameter.

T50 is particularly a time when the bilirubin elimination rate hasincreased to the half-maximal KEMAX.

The Hill coefficient is particularly estimated from a populationapproach, and can assume positive values.

According to this embodiment, the time-varying elimination rate Kelim(t)comprises a model parameter KEMAX, that has to be estimated for theneonate based on its associated covariates. For the bilirubinelimination rate, the model parameter is a maximum stimulation rate ofbilirubin.

While it is possible to assign T50 as a model parameter too, it issufficient for describing the bilirubin level of the neonate, if onlyKEMAX is a model parameter. The influence of the covariates on T50 canbe compensated by other model parameters.

Even if there is no covariate associated to T50, an individualestimation for this parameter based on the bilirubin observations can bemade.

According to another embodiment of the invention, PT(t) is expressed asPT(t)=KP·S(t),  (Eq. 4)

wherein KP is a model parameter comprised by the plurality of modelparameters and particularly wherein S(t) is a time-varying step functionindicating the times where phototherapy has been received by theneonate, particularly wherein S(t) assumes only two values, particularlyvalues of 0 or 1.

The time dependency of PT particularly takes the form of a stepfunction. This way it can be for example modelled that for times whenphototherapy has been received S(t) assumes the value 1, and for timeswhen no phototherapy has been received S(t) assumes the value 0.

PT particularly accounts for the effect of received phototherapyintervals but can also take into account the effect of a phototherapythat might be administered to the neonate in the future.

Equation Eq. 1 models the bilirubin levels in the neonate so accurate,that phototherapy effects can be accounted for. This way it is possibleto quantify the effect of phototherapy on the neonate.

Even more, as the method according to the invention allows for theestimation of bilirubin levels in the future, neonates being at risk ofexhibiting too high of bilirubin levels in the future, can be treatedwith phototherapy pre-emptively, and even more, the duration and timepoint of treatment with phototherapy can be chosen ideally.

According to another embodiment of the invention, the at least onecovariate from the plurality of covariates for estimating the modelparameter comprises one of the following information about the neonatalproperty or the incorporated combination of covariates have at least twoof the following information:

-   -   A birth weight, particularly as a continuous covariate,    -   A gestational age, particularly as a continuous covariate,    -   A delivery mode, particularly as a categorical covariate,        comprising the information whether the neonate was delivered by        Caesarean section or by vaginal delivery;    -   A type of feeding, particularly as a categorical covariate,        comprising the information whether the neonate is fed by mother        milk or by formula milk or parenteral nutrition only;    -   A received phototherapy, particularly as a categorical        covariate, comprising the information whether and when the        neonate has received phototherapy in the past and/or will        receive phototherapy in the future,    -   A weight loss compared to the birth weight, particularly as a        continuous covariate,    -   A low birth weight, as a categorical covariate, comprising the        information whether the birth weight was below 2500 g or above;    -   A respiratory support, particularly as a categorical covariate,        comprising the information whether the neonate has received        respiratory support after delivery or not,    -   A blood incompatibility, particularly as a categorical        covariate, comprising the information whether the neonate had an        ABO blood type incompatibility or a rhesus incompatibility or        both.

Thus, the plurality of covariates can comprise either all of the abovedetailed information or only selected information of the above listedinformation, wherein each covariate comprises particularly only one suchinformation.

The covariate information listed above is allowing for estimating theindividual model parameters of the model function to a sufficiently highdegree, such that the bilirubin level can be estimated for the neonate.

Furthermore, the listed information is particularly easy accessible forany neonate.

A categorical covariate is a covariate that comprises information inform of a discrete category. For example a categorical covariate canprovide information in form of two values, each value representing acategory. The covariate cannot assume any value between the two values.

In contrast to a categorical covariate, a continuous covariateparticularly comprises information in form of a continuous variable thatcan assume a plurality values, and wherein the values are not predefinedby a category.

The term “respiratory support” in the context of the description refersto a neonate that for example has received oxygen enriched air.Respiratory support is particularly needed often for many days, when thelung of the neonate is immature or when the lung is compromised byinfection and other diseases. Respiratory support is provided by amachine.

According to another embodiment of the invention, the model parameter

-   -   Kin_(Base) is estimated from the covariate comprising the        information on the delivery mode, particularly wherein        Kin_(Base) is lower, if the neonate was born by Caesarean        section as compared to a neonate that was born by vaginal        delivery;    -   K_(PNA) is estimated from the covariates comprising the        information about weight loss, the low birth weight, type of        feeding, and a received phototherapy, particularly wherein        K_(PNA) is lower, if the neonate received phototherapy as        compared to a neonate that has not received phototherapy;    -   KEMAX is estimated from the covariate comprising information        about the type of feeding, particularly wherein particularly        KEMAX is lower if the neonate is fed with mother milk as        compared to a neonate that has been fed by formula milk; and/or    -   KP is estimated from the covariate comprising information about        the respiratory support, particularly wherein KP is higher, if        the neonate did not receive respiratory support as compared to a        neonate having received respiratory support.

According to another embodiment of the invention, each modelparameter(s) P from the plurality of model parameters or almost every,i.e. a plurality of model parameter(s) P from the plurality of modelparameters is estimated from the at least one covariate COV_(i) byweighting an associated population model parameter P₀ of the modelparameter P with the at least one covariate COV_(i), particularlywherein each model parameter P is determined byP=P₀·(1+θ·(COV_(i)−median(COV))), if the covariate is a continuouscovariate and by P=P₀·(1+θ·COV_(i)), if the covariate is a categoricalcovariate, wherein θ is a weighting factor adjusting the weight of thecovariate with respect to the respective model parameter.

As already mentioned above, the provision of a previously estimatedpopulation model parameter, allows to express the model parameter interms of a deviation of the associated covariate from an average valuefor the covariate, or from the categorical covariate directly.

While in the context of the specification, a model parameter isparticularly a parameter that depends on at least one covariate or thatis based or derived from at least one covariate, other parameters mightalso be used to generate the model function, wherein said otherparameters might not depend on a covariate.

For each model parameter P, θ can have a different value. Thecategorical covariate is particularly expressed as either being 0 or 1.

According to another embodiment of the invention, the individualparameters and expected bilirubin level of the neonate is furtherdetermined by a maximum a posteriori probability estimate method (MAP),processing the acquired bilirubin levels for the neonate and thebilirubin model function with the determined model parameters,particularly wherein a probability distribution for each model parameteris provided to the maximum a posteriori estimate method, particularlywherein the probability distribution is a log-normal distributionparticularly centred the around the population model parameter.

The statistical method of determining a maximum a posteriori probabilityestimate is particularly based on Bayesian statistics configured fortaking into account a prior probability distribution, particularlycorresponding to the associated probability distribution of the modelparameters and the model function with the determined model parametersand particularly its associated resulting probability distribution, anda plurality of observations, corresponding to the acquired series ofbilirubin levels.

According to Bayesian statistics this information is sufficient toobtain a point estimate, which corresponds to the expected bilirubinlevels for the neonate.

MAP allows for individually estimating and predicting the expectedbilirubin level of the neonate.

The acquired and determined covariates, model parameters and modelfunction as well as the acquired series of bilirubin levels areconfigured for being processed by the MAP. Together with the structuralmodel that describes the typical time course of bilirubin in neonatesand the incorporated covariate effects in the model the MAP allowsforecasting of an individual bilirubin time course, i.e. it particularlypermits to predict bilirubin values for a given individual neonaterather than just making predictions at the population or subpopulationlevel or comparing observed values in an individual neonate withpredicted population average values. Further, the method according tothe invention permits to forecast a time series of bilirubin values(i.e. entire bilirubin profiles up 7-10 days can be predicted) not justone bilirubin value at a certain time point. The method according to theinvention can help caregivers to individualize treatment strategies forneonates with jaundice (e.g. decision support tools).

According to another embodiment of the invention, the bilirubin levelsof the acquired series of bilirubin levels are acquired particularlyfrom the samples during a course of at least 2 days, and wherein atleast two bilirubin levels are estimated, more particularly wherein 3 or4 bilirubin levels are estimated, more particularly more than 4bilirubin levels.

This embodiment allows for a precise estimation of the expectedbilirubin level. The more bilirubin levels are acquired for differenttime points the more accurate the method according to the inventiondetermines the expected bilirubin level.

According to another embodiment of the invention, the bilirubin levelsform the acquired series of bilirubin levels are estimated from asample, particularly a blood sample, obtained from the neonate.

According to another embodiment of the invention, a maximum bilirubinlevel is provided, wherein if, particularly for any given time in thefuture, the expected bilirubin level is higher than the maximumbilirubin level, the neonate is exposed to phototherapy, particularlyfor a determined time interval.

This embodiment allows predicting an expected bilirubin level that ishigher than a predefined maximum bilirubin level.

While the maximum bilirubin level differs between countries, the maximumbilirubin level has particularly a lower limit for preterm neonates thanterm neonates in almost all national guidelines. The maximum bilirubinlevel can be for example the maximum bilirubin level for Germany,France, Great Britain, or the United States of America, particularly forpreterm neonates.

According to another embodiment of the invention, the time interval forphototherapy exposure is estimated by the method according to theinvention, particularly wherein the phototherapy during the timeinterval is taken into account, particularly with the phototherapyexposure function PT, when determining the expected bilirubin level.

This embodiment allows for the precise determination of the effect ofphototherapy.

According to another embodiment of the invention, the expected bilirubinlevel is estimated for a time interval of less than 15 days from birthof the neonate.

The problem according to the invention is also solved by a computerprogram for predicting an expected bilirubin concentration of a neonate,wherein the computer program comprises computer program code, whereinwhen the computer program is executed on a computer, the computerexecutes the method according to the invention.

The term ‘computer’, or system thereof, is used herein as ordinarycontext of the art, such as a general purpose processor or amicro-processor, RISC processor, or DSP, possibly comprising additionalelements such as memory or communication ports. Optionally oradditionally, the terms ‘processor’ or ‘computer’ or derivatives thereofdenote an apparatus that is capable of carrying out a provided or anincorporated program and/or is capable of controlling and/or accessingdata storage apparatus and/or other apparatus such as input and outputports. The terms ‘processor’ or ‘computer’ denote also a plurality ofprocessors or computers connected, and/or linked and/or otherwisecommunicating, possibly sharing one or more other resources such as amemory.

The terms ‘Computer program’ or ‘computer program code’ denote one ormore instructions or directives or circuitry for performing a sequenceof operations that generally represent an algorithm and/or other processor method. The program is stored in or on a medium such as RAM, ROM, ordisk, or embedded in a circuitry accessible and executable by anapparatus such as a processor, a computer or other circuitry.

The processor and program may constitute the same apparatus, at leastpartially, such as an array of electronic gates, such as FPGA or ASIC,designed to perform a programmed sequence of operations, optionallycomprising or linked with a processor or other circuitry.

In the context of embodiments of the present disclosure, by way ofexample and without limiting, terms such as ‘operating’ or ‘executing’imply also capabilities, such as ‘operable’ or ‘executable’,respectively.

In the following, the invention is explained in detail with reference toexemplary embodiments shown in the figures. It is being noted that thedrawings are not necessary to scale.

BRIEF DESCRIPTION OF THE DRAWINGS

In FIG. 1 a concept of the model-function describing postnatal bilirubinlevels and phototherapy effect in preterm neonates is shown. Theneonatal hyperbilirubinemia can be seen as an imbalance betweenincreased production and decreased elimination. Based on neonatalphysiology, Kprod and Kelim change over time. Bilirubin production rateis maximal at birth because of the initial high red blood cellshemolysis, and then decreases to normal elimination rates as can beobserved in heathy adult. Bilirubin elimination rate increases with agecorresponding to the maturity/ontogeny of hepatic function.Transcutaneous phototherapy can increase the elimination rate ofbilirubin.

In FIG. 2 simulations of postnatal bilirubin changes for two scenariosare shown. The dashed curves correspond to a “best case” scenario with10^(th) and 90^(th) percentiles (outer lines) of the simulations and the50^(th) percentile (middle line). The best case scenario is defined bythe following covariates: neonate with a birth weight of 1880 gdelivered by Caesarean section, who lost 6% of his birth weight, fedwith formula milk, without respiratory support and who did not receivephototherapy. The solid curves correspond to a “worst case” scenariowith 10^(th) and 90^(th) percentiles of the simulations (outer lines)and the 50^(th) percentile line (in the middle). The worst case scenariois defined by the following covariates: neonate with a birth weight of1100 g, vaginally delivered, who lost 15% of his birth weight, fed withmother milk, with respiratory support and who received phototherapy at80 hours.

In FIG. 3A individual predictions of time-dependent bilirubin productionrates for two populations of neonates are shown. In FIG. 3B individualpredictions of time-dependent bilirubin elimination rates for twopopulations of neonates are shown. The individual predictions of FIG.3A: bilirubin production rates, Kprod, and FIG. 3B: bilirubinelimination rates, Kelim, for neonates who received phototherapytreatment (black crosses) and neonates who did not receive phototherapy(black circles) are plotted against time. Each point (cross or circle)corresponds to Kprod or Kelim for a given neonate at a given time. Thedashed and solid curves correspond to a smooth curve of all data inneonates with and without phototherapy, respectively.

In FIG. 4A and FIG. 4B a visual Predictive Check to evaluate thepredictive performance of the method according to the invention isshown. Bilirubin levels are plotted against time for FIG. 4A: neonateswho did not receive phototherapy treatment, and FIG. 4B: neonates whoreceived phototherapy. Dashed curves correspond to the simulatedconfidence interval (95%) of the median and the 10^(th) and 90^(th)percentiles. The solid curves are the observed median and 10^(th) and90^(th) percentiles.

In FIG. 5 observed individual bilirubin profiles (series of bilirubinlevels) versus time are shown. Each curve corresponds to one neonate.The x-axis is the time (in hours) since birth and the y-axis is themeasured bilirubin concentration (in μmol/L).

FIG. 6A to FIG. 6F show the influence of a specific covariate on theassociated model parameter.

FIG. 6A shows the influence of the covariate comprising the informationabout the delivery mode on the model parameter Kin_(Base). The solidcurve corresponds to a simulated neonate born by Caesarean section andthe dashed curve to a neonate vaginally delivered.

FIG. 6B shows the influence of the covariate comprising the informationabout the weight loss on the model parameter K_(PNA). The solid, longdashed, dashed and dotted curves correspond to simulated neonates with amaximum weight loss from baseline of −15%, −10%, −5% and 0%,respectively.

FIG. 6C shows the influence of the covariate comprising the informationabout the type of feeding on the model parameter K_(PNA) and KEMAX. Thesolid curve corresponds to simulated data for neonates fed by formulamilk and the dashed curve to a breastfed neonate.

FIG. 6D shows the influence of the covariate comprising the informationabout the low birth weight on the model parameter BILI0. The dashedcurve corresponds to a simulated neonate with a low birth weight (<2500g), and the solid curve to a neonate with a birth weight>2500 g.

FIG. 6E shows the influence of the covariate comprising the informationabout the birth weight on the model parameter K_(PNA). The dotted,dashed, long dashed and solid curves correspond to simulated neonateswith a birth weight of 3100 g, 2600 g, 1600 g and 1100 g respectively.

FIG. 6F shows the influence of the covariate comprising the informationabout the respiratory support on the model parameter KP. The solid curvecorresponds to a simulated neonate without respiratory support and thedashed cure to a neonate with respiratory support. They both receivedone phototherapy cycle at 80 hours.

FIG. 7A shows goodness-of-fit plots, namely measured bilirubin levelsplotted against individual predictions. FIG. 7B shows goodness-of-fitplots, namely measured bilirubin levels plotted against populationpredictions. The black line corresponds to the identity line. On thex-axis the predicted bilirubin levels are plotted, and on the y-axis themeasured bilirubin levels are plotted. The method according to theinvention exhibits a narrow distribution.

FIG. 7C shows goodness-of-fit plots, namely conditional weightedresiduals (CWRES) plotted against population predictions. FIG. 7D showsgoodness-of-fit plots, namely conditional weighted residuals (CWRES)plotted against time. The horizontal line corresponds to y=0.

FIG. 7E shows the predicted and measured bilirubin levels of individualneonates (ID: 1 to ID: 16). Bilirubin levels are plotted against timefor the specific neonate. Dots correspond to observed (measured)bilirubin values. Solid curves are the individual predicted bilirubinlevels estimated with the method according to the invention and dashedcurves correspond to the population predicted profiles.

FIG. 8A shows the observed (measured) bilirubin levels plotted againstforecasted bilirubin levels after 2 days of life. The solid linecorresponds to the identity line. On the x-axis the forecasted bilirubinlevel is plotted, and on the y-axis the measured bilirubin level isshown.

FIG. 8B shows bilirubin observations plotted against the firstforecasted value after the first phototherapy cycle. The solid linecorresponds to the identity line.

Objectives of this invention are to

-   -   (i) provide a method and a model function describing the        physiological patterns of bilirubin level during the first weeks        of life in preterm neonates particularly with        hyperbilirubinemia;    -   (ii) characterize and quantify the effect of phototherapy on        bilirubin kinetics and levels;    -   (iii) identify and quantify relevant covariates that influence        the bilirubin level in a neonate, and    -   (iv) utilize the existing model to develop a bedside decision        support tool that help caregivers to further individualize and        enhance management of preterm neonates with jaundice.

A total of 95 late preterm neonates with physiological jaundicereceiving phototherapy or not has been used to test the method accordingto the invention. From the reviewed 95 neonates, 5 patients withinsufficient number of bilirubin observations (less than 3 acquiredbilirubin levels in the series) and 2 neonates with aberrant bilirubinlevels (profiles) have been excluded. Thus, a total of 88 neonates areused for the evaluation and testing of the method according to theinvention.

The method according to the invention is designed to predictlongitudinal bilirubin data, i.e. expected bilirubin levels, frompreterm neonates with hyperbilirubinemia during their first weeks oflife.

Postnatal bilirubin levels can be described with a turnover model,considering the bilirubin level as a function of the time-dependentrates of a bilirubin production, Kprod and a first-order bilirubinelimination, Kelim, as described in FIG. 1 .

As can be seen in FIG. 1 , Kprod and Kelim change over time, i.e. theychange with increasing postnatal age (PNA). The bilirubin productionrate Kprod is maximal at birth, particularly because of the initial highred blood cell's (RBC) hemolysis, due to the higher RBCs turnover andshorter lifespan in neonates. It decreases to a normal production ratefor a healthy adult within 10 days.

The bilirubin elimination rate Kelim increases with time correspondingto the maturity/ontogeny of hepatic function in the neonate. Differenttime-dependent functions have been tested such as linear, exponential orsaturable Emax for Kelim. It turns out that the saturable Emax functiondescribes the bilirubin elimination most accurate.

In FIG. 1 the effect of phototherapy on the bilirubin level has not beentaken into account.

If a transcutaneous phototherapy effect is taken into account, the modelfunction comprises an additional term PT(t) that is associated to thebilirubin elimination.

In the model function, the bilirubin production rate, Kprod, is modelledas a decreasing age-dependent exponential function (c.f. FIG. 1 , leftpanel). An additional constant bilirubin production rate KAD is added tothe exponential function to reflect the adult production of bilirubin.The elimination rate, Kelim, is modelled with an increasingage-dependent Emax function to describe the ontogeny of hepatic function(c.f. FIG. 1 , right panel). Transcutaneous phototherapy is assumed toincrease the elimination of bilirubin.

The model function can be described with the following equation:

${\frac{d}{dt}{Bilirubin}} = {{{Kpro}{d(t)}} - {( {{{Kelim}(t)} + {P{T(t)}}} ) \cdot {{Bilirubin}(t)}}}$with: Kprod(t) = Kin_(Base) ⋅ exp (−K_(PNA) ⋅ t) + KAD${{Kelim}(t)} = \frac{{KEMAX} \cdot t^{H}}{{T50^{H}} + t^{H}}$Bilirubin(0) = BILI 0 PT(t) = KP ⋅ S(t)

Kprod (t) in units of (μmol·L⁻¹·hour⁻¹) and Kelim(t) in units of(hour⁻¹) are the time-dependent bilirubin production rate and bilirubinelimination rate, respectively. t is the time, corresponding to thepostnatal age (PNA) measured in the units of (hour). Bilirubin(t)represents the bilirubin concentration (μmol·L⁻¹) at the time t. KP(hour⁻¹) is the additional bilirubin elimination rate constantaccounting for the effect of phototherapy on Kelim(t). S(t) represents abinary function equal to 0, when the neonate is not under phototherapyat the time t, and equal to 1 if the neonate receives phototherapy atthe time t. Kin_(Base) (μmol·L⁻¹·hour⁻¹) is the basal neonatal bilirubinproduction rate in addition to the adult bilirubin production rate KAD(μmol·L⁻¹·hour⁻¹). K_(PNA) defines the shape of the time-dependentbilirubin production rate. KEMAX (hour⁻¹) is the maximum stimulation ofbilirubin elimination rate, T50 (hour) the time at which Kelim(t) equals50% of KEMAX and H (dimensionless) is the Hill coefficient determiningthe steepness of the time-dependent rate of bilirubin elimination. Theinitial condition of bilirubin at time 0 h is estimated with theparameter BILI0 (μmol·L⁻¹), as commonly done in pharmacometric modelling[2]. Inter-individual variability (IIV) is estimated on Kin_(Base),BILI0, KEMAX, T50, K_(PNA) and KP. The data does not support estimationof IIV on H and thus is fixed to 0 for H. For the population approach,log-normal parameter distributions are assumed, and a mixed error model,combining additive and proportional components, is used to reflectresidual variability, including measurement errors in acquired bilirubinlevels.

Covariates

The influence of a covariate, i.e. factors that influence bilirubinchanges on a specific model parameter can be tested utilizing a standardstepwise forward selection—backward deletion approach as known from thestate of the art.

The covariate—model parameter relationships/dependencies for acategorical covariate COV_(cat) with two possible conditions (0 or 1) isP=P₀·(1+θ ·COV_(cat)), and for a continuous covariate COV_(cont) thecovariate—model parameter relationships/dependencies isP=P₀·(1+θ·(COV_(cont)−median(COV_(cont)))) with P₀ the typical value ofthe model parameter P, i.e. P₀ is the population model parameter, for aneonate with a covariate equal to the reference value (COV_(cat)=0 orCOV_(cont)=median(COV_(cont)) and θ the estimated parameter describingthe magnitude of the covariate-model parameter relationships.

The covariates can also be used to account for a so-called populationeffect (neonates who received phototherapy versus neonates who did notreceive phototherapy).

For this purpose a mixture model can be evaluated. The mixture modelallows the use of multimodal distribution of model parameters in case ofdifferent subpopulations, and thus assumes that one fraction of thepopulation has one set of population model parameters while theremaining fraction has another set of population model parameters,depending on the value of the associated covariate.

Such a population effect (neonates who received phototherapy versusthose who did not receive phototherapy) can be found on K_(PNA).

Therefore, the model parameter K_(PNA) has two associated populationmodel parameters depending on the value of the associated covariate(here the categorical covariate comprising the information whether theneonate has received phototherapy).

None of the available covariates is able to replace or compensate forthe population effect on K_(PNA). A mixture model on K_(PNA) cantherefore be used in the model function, assuming that 50% of neonateshave the typical value of K_(PNA) equal to K_(PNA0), while the other 50%has the typical value K_(PNA1). The fraction of individuals belonging toeach subpopulation is fixed to 50%. K_(PNA0) and K_(PNA1) can beestimated. The major part of the inter-individual variability (IIV) onK_(PNA) is explained by covariates and the mixture model and is thusfixed to a low value of 5%.

Individual predictions of time-dependent bilirubin production rates,Kprod, and bilirubin elimination rates, Kelim, for both neonates whoreceived phototherapy treatment and those who did not receivephototherapy are plotted in FIG. 3 . A separation between the twopopulations for the time-dependent bilirubin production rate Kprod canbe clearly distinguished (c.f. FIG. 3A), while there is no differencefor the time-dependent bilirubin elimination rate Kelim (c.f. FIG. 3B).Indeed, K_(PNA) is higher in the group without phototherapy leading to asteeper decrease in Kprod compared to the group with phototherapy.

The other covariates do not require taking into account the populationeffect.

The model parameter Kin_(Base) is higher in neonates born by vaginaldelivery leading to higher bilirubin values compared to those born byCaesarean sections (FIG. 6A). Neonates with low birth weight having ahigher baseline bilirubin (BILI0) (FIG. 6D). Increased weight loss andbirth weight and mother milk feeding are associated with lower values ofK_(PNA) (FIG. 6E), so longer time for Kprod to reach adult values andthus higher bilirubin levels. Mother milk feeding is associated withlower maximum stimulation of bilirubin elimination rate (KEMAX) (FIG.6C), and thus slower bilirubin elimination. Finally, the effect ofphototherapy on bilirubin elimination (KP) is reduced in neonates withrespiratory support (FIG. 6F). All these covariate-model parametereffects on the weight changes of a typical neonate are illustrated inFIGS. 6A to 6F.

In FIG. 2 postnatal bilirubin levels of two scenarios of neonatesexhibiting specific covariates are illustrated. As can be seen from theresults of 1000 simulations, a first scenario leads (i) to lowerbilirubin levels compared to a second scenario (ii).

-   -   (i) “best case” scenario of a newborn with a birth weight of        1880 g delivered by Caesarean section, who lost 6% of his birth        weight, fed with formula milk, without respiratory support and        who did not receive phototherapy;    -   (ii) (ii) “worst case” scenario of a newborn with a birth weight        of 1100 g vaginally delivered, who lost 15% of his birth weight,        fed with mother milk, with respiratory support and who received        phototherapy at 80 hours.

Estimates for population model parameters and their IIV from the modelfunction are provided in Table 2. RSE of population model parameters andcorresponding IIV values demonstrate acceptable precision of saidparameters.

TABLE 2 Parameter estimates of the final model. RSE RSE estimate IIV IIVParameter (unit) Estimate (%) (% CV) (%) Kin_(Base) (μmol/L/hour) 2.8 713 20 BILI0 (μmol/L) 15.4 19 34 11 KEMAX (hour⁻¹) 0.009 18 47 18 T50(hour) 110 6 24 16 H 8.98 30 0 FIX — K_(PNA0) (hour⁻¹) 0.0099 19 5 FIX —K_(PNA1) (hour⁻¹) 0.022 13 5 FIX — KP (hour⁻¹) 0.022 13 47 17 KAD(μmol/L/hour) 0.43 30 0 FIX — Vaginal delivery effect on KinBase 0.29 23— — Weight loss effect on KPNA 0.028 44 — — Birth weight effect on KPNA−0.0002 55 — — Mother milk effect on KPNA −0.26 34 — — Low birth weighteffect on BILI0 1.16 35 — — Mother milk effect on KEMAX −0.28 45 — —Respiratory support effect on KP −0.42 24 — — Probability for mixturemodel 0.5 FIX — — — Residual error: additive 0.099 11 — — Residualerror: proportional 3.68 21 — — CV: coefficient of variation; FIX: fixedparameter; IIV: inter-individual variability; RSE: relative standarderror.

The typical baseline bilirubin (BILI0) is estimated at 15.4 μmol·L⁻¹ ina neonate with a birth weight>2500 g and at 33.26 μmol·L⁻¹ in a neonatewith a birth weight<2500 g. The typical (i.e. the average populationparameter) total basal production rate of bilirubin Kin_(Base)+KAD isestimated at 3.23 μmol·L⁻¹·hour⁻¹ in a typical neonate delivered byCaesarean section and at 4.05 μmol·L⁻¹·hour⁻¹ in a typical neonatevaginally delivered. The maximum stimulation of bilirubin eliminationrate (KEMAX) is estimated to be slowed by one-half (T50) at a typicalage of 110 hours. K_(PNA0) is estimated to be equal to 2.2 timesK_(PNA1) (0.022 hour⁻¹ versus 0.0099 hour⁻¹). The time-dependentbilirubin elimination rate is increased by 0.022 hour⁻¹ in neonateswithout respiratory support and by 0.013 hour⁻¹ in neonates withrespiratory support.

Prediction and Estimation of Individual Bilirubin Levels According tothe Method of Invention

Two different predictions or estimations can be made with the methodaccording to the invention:

-   -   (i) A forecast/projection of individual bilirubin time courses        (or profiles) after few days of life, and    -   (ii) An early prediction of the risk for receiving phototherapy.

The model function with covariates and associated model parameters isapplied to the series of acquired bilirubin levels (particularlyacquired from a sample of the neonate within the first two days of life)in order to forecast individual bilirubin levels up to two weeks oflife. A maximum a posteriori Bayesian method (MAP) is used to predict orforecast bilirubin levels for a individual neonate withhyperbilirubinemia. The same MAP method can be applied to forecast thebilirubin level after a first phototherapy cycle.

The maximum a posteriori (MAP) Bayesian method uses a point estimate ofthe mode of model parameters' posterior density, corresponding to theproduct of a prior (model function and population parameters' log-normaldistributions) and a likelihood (residual error model).

Individual bilirubin predictions can be graphically compared with anobserved bilirubin level. The predictive performance can numerically beevaluated by calculating mean percentage error (MPE) to assessprediction bias and mean absolute percentage error (MAPE) and root meansquared error (RMSE) to estimate prediction accuracy [1].

The mean percentage error (MPE), mean absolute percentage error (MAPE)and root mean squared error (RMSE) can be calculated to evaluate biasand accuracy of the predictions:

${{{MPE}\mspace{11mu}(\%)}:{MPE}} = {\frac{1}{n}{\sum{\frac{( {{Obs} - {Pred}} )}{Obs} \times 100}}}$${{{MAPE}\mspace{11mu}(\%)}:{MAPE}} = {\frac{1}{n}{\sum{\frac{{{Obs} - {P{red}}}}{Obs} \times 100}}}$${{{RMSE}\mspace{11mu}(g)}:{RMSE}} = \sqrt{\frac{1}{n}{\sum( {{Obs} - {Pred}} )^{2}}}$

Wherein, n is the number of observations.

Acquired series of bilirubin levels plotted against forecasted valuesafter the first two days of life show acceptable graphical agreement(FIG. 8A). Precision of forecasted values are acceptable (MAPE [95% CI]:23.0% [19.8%-26.2%], RMSE=44.4 μmol·L⁻¹) and bias is limited (MPE [95%CI]: −4.5% [−8.3%-−0.6%]), with an absolute mean error magnitude betweenobserved weights and forecasted weights of only 1.43%, or 33.7 μmol·L⁻¹[95% CI: 30.8 μmol·L⁻¹-36.5 μmol·L⁻¹]. CI stands for confidenceinterval.

The method according to the invention can also be applied to forecast afirst bilirubin level measurement just after the first phototherapycycle. Observed bilirubin level data plotted against the firstforecasted bilirubin level after the first phototherapy cycle shows goodgraphical agreement (see FIG. 8B). Precision of forecasted values areacceptable (MAPE [95% CI]: 18.3% [12.2%-24.5%], RMSE=33.7 μmol·L⁻¹) andbias is limited (MPE [95% CI]: −8.5% [−16.3%-−0.6%]),

The second objective of the invention is to early identify aberrantbilirubin levels or trends that may precede treatment with phototherapy.For that, the probability of receiving phototherapy treatment can belinked with predictors using logistic regression.

Different predictors can be evaluated in univariate and multivariatemodels:

-   -   (i) all the available neonatal and maternal characteristics and    -   (ii) the predicted bilirubin levels from the method according to        the invention based on an individual series of acquired        bilirubin levels during the first two days of life.

The ability of the method according to the invention, includingsignificant predictors, to differentiate neonates who receivedphototherapy from those who did not receive phototherapy can beevaluated with a ROC (Receiver operating characteristic) curve bycalculating the sensitivity and specificity.

Among all the available individual characteristics, only the binaryfactor very low birth weight (birth weight<1500 g versus birthweight>1500 g) is significant. Results from the ROC curve show that thelogistic regression method is not able to discriminate neonates whoreceived phototherapy from those who did not receive phototherapy(AUC=0.59, sensitivity=23%, specificity=95%).

Significant predictors in multivariate logistic regression include:K_(PNA), Kin_(Base), BILI0 and the very low birth weight. Results fromthe ROC curve show that a cut-off of 0.6 for the results from thelogistic regression method is able to discriminate neonates who receivedphototherapy from those who did not receive phototherapy with asensitivity of 72% and a specificity of 85% (AUC=0.87).

Computing Process

The software NONMEM 7.3 (ICON Development Solutions, Ellicott City, Md.,USA) can be used to fit individual bilirubin data to the model function.Estimations can be made by maximizing the likelihood of the data, withthe first-order conditional estimation (FOCE) algorithm withinteraction. Data handling, graphical representations, numericalcriteria calculations, logistic regressions and ROC curves can beperformed with an appropriate computer language.

Longitudinal bilirubin data with a median [minimum-maximum] of 8 [3-15]observations per individual up to a median [minimum-maximum] of 183hours [29-320] of life are available. Neonates are all moderate to latepreterm with a GA of 33.3 weeks [32.0-34.8] and a birth weight of 1880 g[1050-3500]. Among these neonates, 47 received at least one cycle ofphototherapy and 41 neonates did not receive any phototherapy. The timeof the start of each phototherapy cycle and the duration is known.

All individuals' series of bilirubin levels are represented in FIG. 5 .In the method according to the invention, the time 0 corresponds to thetime of birth.

Individual characteristics of neonates are summarized in Table 1.

TABLE 1 Summary of individual characteristics. Median [Minimum-Maximum]Characteristics Number of individuals (%) Number of neonates 88 Time offollow up (hours) 183 [29-320] Time of follow up (days) 7.6 [1.2-13.3]Number of bilirubin observations per individual 8 [3-15] Baselinebilirubin (μmol/L) 42 [13-92] Number of cycle of phototherapy: 0 41(47%) 1 28 (32%) 2 15 (17%) 3  4 (4%) Duration of phototherapy (hours)24 [8-59] Birth weight (g) 1880 [1050-3500] Low birth weight: birthweight <2500 g: yes 84 (95%) no  4 (5%) Very low birth weight: birthweight <1500 g: yes 13 (15%) no 75 (85%) Maximum weight loss (%) −5.38[−16.51-0] Gestational age (weeks) 33.3 [32-34.8] Gender: girl 51 (58%)boy 37 (42%) Arterial pH 7.31 [6.88-7.50] Baseline hemoglobin (g/L) 188[134-255] APGAR at 5 minutes: ≤8 55 (63%) >8 33 (37%) Delivery mode:Caesarean section 57 (64%) Vaginal delivery 31 (36%) Prolonged pretermrupture of membrane: yes 22 (25%) no 66 (75%) Multiple pregnancy: single55 (63%) twins or triplets 33 (37%) Treatment with amoxicillin oramikacin: yes 20 (23%) no 68 (77%) Type of feeding: exclusively formulamilk  9 (10%) mother milk (exclusively or 79 (90%) supplementary)Infection: suspected or proven 21 (24%) none 67 (76%) Infant respiratorydistress: yes 44 (50%) no 44 (50%) Respiratory support: yes 40 (45%) no48 (55%) O2 support: yes 19 (22%) no 68 (78%) Mother's age (years) 31[20-40] Mother diseases: none 58 (66%) yes (infection, gestationalhypertension, 30 (34%) PE, HELLP, DM, GDM) Coombs test: Positive  2 (2%)Negative 77 (88%)

Data are presented as median [minimum-maximum] or number of subjects(%).

APGAR 5: Apgar score at 5 minutes; PE: pre-eclampsia; HELLP syndrome:complication of pre-eclampsia; DM: diabetes mellitus; GDM: gestationaldiabetes mellitus.

Neonatal jaundice occurs in literally all newborns and, although in themajority of cases this condition is self-limited, a fraction of neonatesneed to be treated with phototherapy or other medical interventions arerequired. Failure to promptly identify newborns at risk for developingsevere jaundice can lead to life-long neurologic sequelae, includingpotential reduction in IQ score.

The method according to the invention is capable of predicting thephysiological patterns of bilirubin levels during the first weeks oflife in preterm neonates with hyperbilirubinemia. Further, neonatalphysiology in the model development with time-dependent decrease ininput rate (Kprod) and ontogenic effect on the output rate (Kelim) istaken into account.

The method according to the invention is not only able to identify latepreterm neonates that are at risk for hyperbilirubinemia but can alsocharacterize and project effects of phototherapy sessions on individualbilirubin profiles.

Bilirubin charts known from the state of the art show clear limits asthese are not taking the dynamics of bilirubin changes during the firstweeks of life into account and cannot be used to project individualbilirubin profiles.

In contrast, the method according to the invention accounts for bothcovariates and time dependent changes of bilirubin level. As such it canbe applied to predict not just a reference curve from a neonatalpopulation but also individual bilirubin levels during the first weeksof life of a specific neonate. A decision support tool, particularly acomputer program, based on the method according to the invention isexpected and designed to

-   -   (i) allow for a risk-based approach of neonatal        hyperbilirubinemia, thus reducing hospitalization costs,    -   (ii) support health-care professionals in planning appropriate        follow-up strategies for discharged neonates with jaundice,    -   (iii) facilitate planning of early surgical procedures such as        circumcision, and has the potential to    -   (iv) minimize the risk for the need for readmission and longer        term neurological sequelae.

It is noted that the method according to the invention is particularlylimited to late preterm neonates with physiological jaundice receiving(or not receiving) phototherapy. As such the method may particularly notbe used to project bilirubin levels or the risk for phototherapy inother neonatal populations.

The method according to the invention is the first method that describesbilirubin levels and kinetics and phototherapy effects in pretermneonates with physiological jaundice during the first weeks of life. Auser-friendly online tool that can be used to forecast individualbilirubin levels and phototherapy effects is disclosed as well. Saidtool can optimize treatment strategies for neonates with jaundice. Adecision support tool that permits neonatologists to quantitativelyindividualize management of late preterm neonates with jaundice isprovided.

REFERENCES

-   [1] Sheiner L B, Beal S L. Some suggestions for measuring predictive    performance. J Pharmacokinet Biopharm 1981; 9(4):503-12.-   [2] Dansirikul C, Silber H E, Karlsson M. O. Approaches to handling    pharmacodynamic baseline responses. Journal of pharmacokinetics and    pharmacodynamics 2008; 35(3):269-83. doi:    10.1007/s10928-008-9088-2.#-   [3] Berk et al., Studies of bilirubin kinetics in normal adults, J    Clin Invest. 1969

The invention claimed is:
 1. A method of treating physiological jaundicein a neonate, comprising the steps of: a. detecting and identifyingphysiological jaundice in a neonate; and b. exposing the neonate havingphysiological jaundice to phototherapy to treat the physiologicaljaundice; wherein said detecting and identifying comprises calculating abilirubin level in the neonate and determining that the calculatedbilirubin level is higher than a provided maximum bilirubin level, byperforming the steps of: 1) acquiring a series of bilirubin levelsmeasured at different time points from a blood sample obtained from theneonate, 2) acquiring a plurality of covariates from the neonate, eachcovariate comprising an information about a neonatal property, whereinthe information comprises one of the following information: A birthweight, as a continuous covariate, A gestational age, as a continuouscovariate, A delivery mode, as a categorical covariate, comprisinginformation about whether the neonate was delivered by Caesarean sectionor by vaginal delivery; A type of feeding, as a categorical covariate,comprising information about whether the neonate is fed by mother milkor by formula milk; A received phototherapy, as a categorical covariate,comprising information about whether the neonate has receivedphototherapy or not in the past and/or will receive phototherapy in thefuture, A weight loss compared to the birth weight, as a continuouscovariate, A low birth weight, as a categorical covariate, comprisinginformation about whether the birth weight was below or above apredefined birth weight, wherein the predefined weight is 2500 g; Arespiratory support, as a categorical covariate, comprising informationabout whether the neonate has received respiratory support afterdelivery or not, 3) providing a predefined bilirubin model function,wherein the bilirubin model function is configured to describe a timecourse of the bilirubin level of the neonate, 4) determining a pluralityof model parameters of the bilirubin model function, wherein each modelparameter is determined from at least one covariate of the plurality ofcovariates and an associated population model parameter corresponding toa model parameter for a neonate exhibiting average covariates, and 5)obtaining the calculated bilirubin level in the neonate from theacquired series of bilirubin levels and the bilirubin model functionwith the determined model parameters, wherein the calculated bilirubinlevel is a bilirubin level of the neonate for a time later than a lastlyacquired bilirubin level of the series of bilirubin levels, wherein thebilirubin model function is a rate equation relating a time-varyingbilirubin production rate Kprod, with a time-varying bilirubinelimination rate Kelim, and a time-varying phototherapy exposurefunction PT, wherein the bilirubin production rate Kprod, the bilirubinelimination rate Kelim and the phototherapy exposure function PTcomprise the plurality of model parameters.
 2. The method according toclaim 1, wherein the model function is expressed as${\frac{d}{dt}{{Bilirubin}(t)}} = {{{Kpro}{d(t)}} - {( {{Keli{m(t)}} + {P{T(t)}}} ) \cdot {{Bilirubin}(t)}}}$wherein $\frac{d}{dt}$ is a time-derivative operator, whereinBilirubin(t) is the bilirubin level at a time t, wherein Kprod(t) is thebilirubin production rate at a time t, wherein Kelim(t) is the bilirubinelimination rate at a time t.
 3. The method according to claim 1,wherein the bilirubin production rate Kprod(t) is expressed asKprod(t)=Kin_(Base)·exp(—K_(PNA)·t)+KAD, wherein Kin_(Base), and K_(PNA)are model parameters comprised by the plurality of model parameters,wherein Kin_(Ba), is an excess neonatal bilirubin production rate attime zero, wherein KAD is a normal bilirubin production rate, andwherein K_(PNA) is a decay rate of the bilirubin production rateKprod(t), and wherein Kprod(t) is the bilirubin production rate at atime t.
 4. The method according to claim 3, wherein the model parameterKin_(Base) is estimated from the covariate comprising the information onthe delivery mode, wherein Kin_(Base) is lower, if the neonate was bornby Caesarean section as compared to a neonate that was born by vaginaldelivery; and K_(PNA) is estimated from the covariates comprising theinformation about weight loss, the low birth weight, type of feeding,and a received phototherapy, wherein K_(PNA) is lower, if the neonatereceived phototherapy as compared to a neonate that has not receivedphototherapy.
 5. The method according to claim 1, wherein the bilirubinelimination rate Kelim(t) is expressed as${{{Keli}{m(t)}} = \frac{{KEMAX} \cdot t^{H}}{{T50^{H}} + t^{H}}},$wherein Kelim(t) is the bilirubin elimination rate Kelim(t) at a time t,wherein KEMAX is a model parameter comprised by the plurality of modelparameters, and wherein KEMAX is a maximum stimulation rate ofbilirubin, T50 is a time when the bilirubin elimination rate hasincreased to 50% of its value at t=0, wherein H is a Hill coefficient.6. The method according to claim 5, wherein the model parameter KEMAX isestimated from the covariate comprising information about the type offeeding, and wherein KEMAX is lower if the neonate is fed with mothermilk as compared to a neonate that has been fed by formula milk.
 7. Themethod according to claim 1, wherein PT(t) is expressed asPT(t)=KP·S(t), wherein KP is a model parameter determined from thecovariate comprising information about the respiratory support, whereinS(t) is a time-varying step function indicating times when phototherapyhas been received by the neonate, wherein S(t) assumes only two valuesof 0 or 1, and wherein PT(t) is the phototherapy exposure function at atime t.
 8. The method according to claim 7, wherein KP is higher, if theneonate did not receive respiratory support as compared to a neonatehaving received respiratory support.
 9. The method according to claim 1,wherein the plurality of covariates further comprises an informationabout a blood incompatibility, as a categorical covariate, comprisinginformation about whether the neonate has an ABO blood typeincompatibility or a rhesus incompatibility or both.
 10. The methodaccording to claim 1, wherein each model parameter is determined fromthe at least one covariate by weighting the associated population modelparameter of the model parameter with the at least one covariate,wherein each model parameter is determined by P=P₀·(1+θ·(COV_(i)—median(COV))), if the at least one covariate is a continuous covariateand by P=P₀ (1+θ·COV_(i)), if the at least one covariate is acategorical covariate, wherein P is the each model parameter, P₀ is theassociated population model parameter of the each model parameter,COV_(i), is the at least one covariate, median(COV) is a median of theat least one covariate in an associated population comprising a neonateexhibiting average covariates, and θ is a weighting factor for adjustingweight of the at least one covariate on the each model parameter. 11.The method according to claim 1, wherein the calculated bilirubin levelof the neonate is calculated from the acquired series of bilirubinlevels and the bilirubin model function with the determined modelparameters by use of a maximum a posteriori probability estimate method(MAP).
 12. The method according to claim 1, wherein the bilirubin levelsof the acquired series of bilirubin levels are acquired during a courseof at least 24 hours, and wherein at least two bilirubin levels aremeasured.
 13. The method according to claim 1, wherein a time intervalfor phototherapy exposure is estimated when calculating the calculatedbilirubin level.
 14. A computer program for determining a bilirubinconcentration of a neonate, wherein the computer program comprisescomputer program code, wherein when the computer program is executed ona computer, and the computer executes the method according to claim 1.